In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.

What are homotopy classes?

homotopy theory

geometric region is called a homotopy class. The set of all such classes can be given an algebraic structure called a group, the fundamental group of the region, whose structure varies according to the type of region.

What is meant by homotopy?

Homotopy, in mathematics, a way of classifying geometric regions by studying the different types of paths that can be drawn in the region. Two paths with common endpoints are called homotopic if one can be continuously deformed into the other leaving the end points fixed and remaining within its defined region.